I am rebuilding a Trek 2005 model 6500 and my spec. sheet for the bike says it has a Shimano Alivio front derailleur. Where do I find the model no. that should be stamped on the part? I don't see it anywhere on the part. This is a 3 x 8 speed setup.

I believe from images I've seen that the 2005 Trek 6500 had a top pull, low clamp FD.
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DWGKNZOct 16 '13 at 1:02

For what its worth, a lower end FD marketed for a 3x9 setup will probably work with a 3x8 fine with a 8 speed chain (you can run a 9 speed chain on an 8 speed system if you want - its typically fine as well) since the cage probably wasn't narrowed (much) at this spec level. Also, if you have things like sram attack, you can switch between sram and shimano to a further extent (though alivio/acera/altus level parts for 3x8 are cheap enough that you're not going to save any money).
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BatmanOct 18 '13 at 17:34

The three different options here appear to be the FD-M410E, FD-M412 and FD-M413. There are photos of all three (looks like the main difference is the position of the clamp), so you should be able to work out what you have right now.